# Countable Sample Space

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A Countable Sample Space is a Sample Space that is a Countable Set.

**AKA:**Discrete Sample Space.**Context:**- It can be:
- It can be a Finite Sample Space.
- …

**Example(s):**- any Finite Sample Space, such as:
- {Heads,Tails}, the Sample Space of a Coin Toss Experiment.
- {1,2,3,4,5,6}, the Sample Space of a Dice Roll Experiment.

- the Sample Space for the Coin Toss Experiment where the Coin is tossed until a Heads shows up (because the coin could be tossed indefinitely).
- …

- any Finite Sample Space, such as:
**Counter-Example(s):**- The Time Duration [0, ∞) of a Lifetime Experiment, such as how long a Lightbulb will last.
- The Scale of person Heights.

**See:**Continuous Sample Space.

## References

### 2009

- http://www.statistics.com/resources/glossary/c/countnspc.php
**Countable Sample Space:**If a sample space contains finite or countably infinite number of sample points then such a sample space is referred to as a countable sample space.

### 2008

- (Qian) => Gang Qian. (2008). Basic Probability Theory." Lecture Notes: AME 598 Sensor Fusion, Arizona State University, Fall 2008.
- Sample Space (S): defined as the set of all possible outcomes from a random experiment.
- Countable or discrete sample space, one-to-one correspondence between outcomes and integers
- Uncountable or continuous sample space